Non-wave Solutions of the Maxwell-Einstein Equations

Zayko, Yuriy (2014): Non-wave Solutions of the Maxwell-Einstein Equations. Published in: Physical Science International Journal , Vol. 4, No. 9 (November 2014): pp. 1280-1292.

Abstract

This article is devoted to treating of non-wave, i.e. instanton solution for the Maxwell- Einstein equations. Equations for the field of instanton and metric are derived. Metric of pseudo-Euclid space which is corresponding to transition between degenerate classical vacua of problem and is connected with presence at the space infinity divergent and convergent spherical electromagnetic waves is studied. An expression of the instanton is received and it’s size is found. Value of pseudo-Euclid action is calculated. It is shown that instanton violates so called “week energetic condition” which is essential for space-time singularities proving.

• Item Type: MPRA Paper
• Language: English
• Keywords: Instanton; pseudo-Euclid space; classical vacuum; pseudo-Euclid action
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

References

1. Hawking SW. Gravitational instantons. Phys Lett. 1977;60:81.

2. Rajaraman R. An introduction to solitons and instantons in quantum field theory. North-Holland Publishing Company, Amsterdam-NY-Oxford; 1982.

3. Zayko YN. Completeness problems of being transmitted information. Proc of the Saratov State University. 2013;13(2):15-21. Russian.

4. Schvarts АS. Quantum field theory and topology. Мoscow, Nauka; 1989. Russian.

5. Zayko YN. Electromagnetic fields of self-modes in spherical resonators.Physical Science International Journal, 2015, №5(1), pp.18-25

6. Zayko YN. Instanton for the Maxwell-Einstein equations. Available: http://sfm.eventry.org/report/661

7. Zayko YN. Explicit Solution of Einstein-Maxwell equations. International Journal of Theoretical and Mathematical Physics – IJTMP. 2011;1(1). pp.12-16.

8. Landau LD, Lifshitz EM. The classical theory of fields. (4th ed). Butterworth-Heinemann. 1975

9. Arfken G. Mathematical methods for physicists. Academic Press, New York and London; 1966.

10. Prudnikov AP, Brychkov YUA, Marichev OI. Integrals and series Gordon and Breach.New York; 1986;1–3.

11. Vainstein AI, Zakharov DI, Novikov VA, Shifman MA. Instanton alphabet. Uspehi Fizicheskih Nauk. 1982;136(4):553-591. Russian.

12. Hawking SW, Ellis GFR. The large scale structure of space-time. Cambridge Univ Press; 1973.

13. Weber J. Gravitation and Light. In: Chiu HY, Hoffmann WF, editors. Gravitation and Relativity. The New York – Amsterdam: W.A. Benjamin, Inc; 1964.

14. Wheeler JA. Gravitation as Geometry. In: Chiu HY, Hoffmann WF, editors. Gravitation and Relativity. The New York – Amsterdam: W.A. Benjamin, Inc; 1964.

15. Zeldovich YB, Novikov ID. Theory of gravitation and star evolution. Moscow, Nauka; 1971. Russian.

16. Berestetskii VB, Lifshitz EM, Pitaevskii LP. Relativistic quantum theory (1st ed.). Pergamon Press. 1971

17. Cornell University Library. Available: http://arxiv.org.